The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  1  0  1  a (a+1)X  a (a+1)X+1 X+a  1  0
 0  0  1  0 a+1  1  a  a  1  0 X+1 aX+a aX+1  X
 0  0  0  1  1 a+1 a+1  a  0  X X+a+1 (a+1)X (a+1)X+1 (a+1)X
 0  0  0  0 (a+1)X  X aX  X (a+1)X aX  0 (a+1)X  X aX

generates a code of length 14 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+156x^28+132x^29+192x^30+492x^31+1185x^32+1536x^33+1920x^34+2304x^35+8175x^36+10632x^37+9216x^38+12792x^39+33429x^40+30144x^41+18048x^42+26976x^43+47586x^44+30036x^45+13632x^46+6588x^47+5616x^48+1248x^49+99x^52+9x^56

The gray image is a linear code over GF(4) with n=56, k=9 and d=28.
This code was found by Heurico 1.16 in 22.3 seconds.